CMC hypersurfaces with bounded Morse index

Theodora Bourni, Ben Sharp, Giuseppe Tinaglia

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
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Abstract

We provide qualitative bounds on the area and topology of separating constant mean curvature (CMC) surfaces of bounded (Morse) index. We also develop a suitable bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular, we show that convergence always occurs with multiplicity one, which implies that the minimal blow-ups (bubbles) are all catenoids.
Original languageEnglish
Pages (from-to)175-203
Number of pages29
JournalJournal fur die Reine und Angewandte Mathematik
Volume2022
Issue number786
Early online date1 Apr 2022
DOIs
Publication statusPublished - 1 May 2022

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